plumiOCR A‑Level Maths questions by topic
Every question from every OCR A-Level Maths paper, 2018–2025, question by question. Filter by topic, paper or year, open the mark scheme under any question, and download a set as a PDF.
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![June 2025 Paper 1, question 1: Express each of the following in the form pxq, where p and q are constants. 1 2 (a) [1] 4 x ^ h 3 (b) x x [2] 5 3 5 (c) x x [2] 2 8 # ^ h 1 5 6 3 (d) x x [3] 27](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-01-qp.webp?v=3)
![June 2025 Paper 1, question 3: 3 (a) A sequence has terms u1, u2, u3, … defined by u 3 and u u 5 for n H . 1 1 = = - n 1 n + (i) Find the values of u2, u3 and u4. [2] (ii) Describe the behavi](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-03-qp.webp?v=3)
![June 2025 Paper 1, question 4: The position vector of the point A is . 0 5 i 0 5 . j . - (a) Determine whether . 0 5 i 0 5 . j is a unit vector. [2] - (b) Find the direction of . 0 5 i 0 5 .](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-04-qp.webp?v=3)
![June 2025 Paper 1, question 8: 8 (a) Find the first three terms in the expansion of ( 2 )x - in ascending powers of x. [4] + 1 4 x + (b) Hence find the first three terms in the expansion of (](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-08-qp.webp?v=3)
![June 2025 Paper 1, question 9: (a) Express cos 3 2 x 4 sin 2 x in the form R cos ( 2 x ) , where R 2 0 and ° 0 1 1 90 ° . [3] + - a a (b) In this question you must show detailed reasoning. 3](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-09-qp.webp?v=3)
![June 2025 Paper 1, question 12: 4 x + 12 (a) Express ( in partial fractions. [4] x 1 x )( 1 x ) + - d = y 2 4 x + The gradient of a curve is given by and the curve passes through the d x x ( 1](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24001-jun25-12-qp.webp?v=3)
![June 2025 Paper 2, question 1: In this question you must show detailed reasoning. 2 Solve the inequality x 3 x 10 . [3] + G](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun25-01-qp.webp?v=3)
![June 2025 Paper 2, question 2: In this question you must show detailed reasoning. Solve the following equations. 2 3 (a) ( x 5 ) 8 [3] - = 2 3 = y (b) e 2 [2] 4 2 (c) x 3 x 4 0 [4] - - =](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun25-02-qp.webp?v=3)
![June 2025 Paper 2, question 4: / 4 (a) Prove that ( cos sin ) 1 sin 2 . [2] + + i i i cos sin + i i (b) Hence or otherwise prove that sec 2 tan 2 . [4] + i i / cos sin i - i](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun25-04-qp.webp?v=3)
![June 2025 Paper 2, question 6: 3 2 6 A curve has equation y 3 x 4 x 6 x 12 x . = - - + d . y (a) (i) Find x [2] d (ii) Use your answer to part (a)(i) to find the x-coordinates of the stationa](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun25-06-qp.webp?v=3)
![June 2025 Paper 2, question 8: In this question you must show detailed reasoning. 1 y Use integration by parts to find the exact value of 2 ln ( 3 2 x ) d x . [5] - 0](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/h24002-jun25-08-qp.webp?v=3)
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